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Simplicity of algebras associated to étale groupoids

Journal Article


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Abstract


  • We prove that the full C ∗-algebra of a second-countable, Hausdorff, étale, amenable groupoid is simple if and only if the groupoid is both topologically principal and minimal. We also show that if G has totally disconnected unit space, then the complex ∗-algebra of its inverse semigroup of compact open bisections, as introduced by Steinberg, is simple if and only if G is both effective and minimal.

UOW Authors


  •   Brown, Jonathan H. (external author)
  •   Clark, Lisa Orloff (external author)
  •   Farthing, Cynthia (external author)
  •   Sims, Aidan

Publication Date


  • 2014

Citation


  • Brown, J., Clark, L., Farthing, C. & Sims, A. (2014). Simplicity of algebras associated to étale groupoids. Semigroup Forum, 88 (2), 433-452.

Scopus Eid


  • 2-s2.0-84897989497

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3245&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2236

Has Global Citation Frequency


Number Of Pages


  • 19

Start Page


  • 433

End Page


  • 452

Volume


  • 88

Issue


  • 2

Place Of Publication


  • United States

Abstract


  • We prove that the full C ∗-algebra of a second-countable, Hausdorff, étale, amenable groupoid is simple if and only if the groupoid is both topologically principal and minimal. We also show that if G has totally disconnected unit space, then the complex ∗-algebra of its inverse semigroup of compact open bisections, as introduced by Steinberg, is simple if and only if G is both effective and minimal.

UOW Authors


  •   Brown, Jonathan H. (external author)
  •   Clark, Lisa Orloff (external author)
  •   Farthing, Cynthia (external author)
  •   Sims, Aidan

Publication Date


  • 2014

Citation


  • Brown, J., Clark, L., Farthing, C. & Sims, A. (2014). Simplicity of algebras associated to étale groupoids. Semigroup Forum, 88 (2), 433-452.

Scopus Eid


  • 2-s2.0-84897989497

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3245&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2236

Has Global Citation Frequency


Number Of Pages


  • 19

Start Page


  • 433

End Page


  • 452

Volume


  • 88

Issue


  • 2

Place Of Publication


  • United States